An Upper Bound Visualization of Design Trade‐Offs in Adsorbent Materials for Gas Separations: CO2, N2, CH4, H2, O2, Xe, Kr, and Ar Adsorbents

Abstract The last 20 years have seen many publications investigating porous solids for gas adsorption and separation. The abundance of adsorbent materials (this work identifies 1608 materials for CO2/N2 separation alone) provides a challenge to obtaining a comprehensive view of the field, identifying leading design strategies, and selecting materials for process modeling. In 2021, the empirical bound visualization technique was applied, analogous to the Robeson upper bound from membrane science, to alkane/alkene adsorbents. These bound visualizations reveal that adsorbent materials are limited by design trade‐offs between capacity, selectivity, and heat of adsorption. The current work applies the bound visualization to adsorbents for a wider range of gas pairs, including CO2, N2, CH4, H2, Xe, O2, and Kr. How this visual tool can identify leading materials and place new material discoveries in the context of the wider field is presented. The most promising current strategies for breaking design trade‐offs are discussed, along with reproducibility of published adsorption literature, and the limitations of bound visualizations. It is hoped that this work inspires new materials that push the bounds of traditional trade‐offs while also considering practical aspects critical to the use of materials on an industrial scale such as cost, stability, and sustainability.


Data gathering method
This section outlines the literature search and data processing methods used.

Literature search
The search was performed on 16/11/2021 using the "Research topic" function of SciFinder.

Data extraction notes
Papers required experimental results for at least two gases to be considered in the review. This meant that papers that only showed simulations results or only reported the adsorption of a single gas were not considered.
Where values were extracted from figures, they were estimated by eye. The most accurate method would be to digitize the plots to extract the values of interest, however, the scale of this review meant that this was not feasible.
Students reviewing references for this review were first taken through 13 example papers to help them understand the process. The examples were split into two sections. The first section was worked through in detail with the students one on one, the second section was completed by the student on their own afterwards. The second section aimed to confirm the students understanding. After successful completion of the second section, they began work on references for the review.

Data gathered
This section describes the specific data gathered for each material/gas separation pair.

General information
 Adsorbent class (Porous, non-porous, porous+metal site, MOF, MOF+metal site).  Selective and non-selective gas.  Isotherm temperatures.  BET surface area

Selectivity and capacity
 Temperature and pressure that capacity and selectivity correspond to. This temperature was chosen as close to 293 K and 100 kPa as possible to give a fair comparison between materials.  Pure gas capacity for selective gas.  Selectivity.  The method used for calculating selectivity was also recorded. Selectivity method: a) Using IAST for an equimolar amount of the two gases (preferred over uptake ratio). b) From reported adsorption capacities of both gases (uptake ratio).  c) Measured/calculated using an unconventional method. d) Measurement method not shown/available. l) Henrys law.
In the case that a paper did not report a selectivity value, it was calculated manually using the reported gas uptake and the uptake ratio method.

Heat of adsorption
 Heat of adsorption for both the selective and non-selective gas.  The heat of adsorption was recorded at the Temperature and Pressure previously recorded for selectivity and capacity. If the heat of adsorption was reported as a function of loading, the loading value was chosen as the loading at the Temperature and Pressure previously recorded for selectivity and capacity.  If the loading was below/above the minimum/maximum loading value of the heat of adsorption curve, report the heat of adsorption at the minimum/maximum loading shown on the heat of adsorption curve.  "n/a" was recorded if the paper did not report heat of adsorption for the gas of interest  Heat of adsorption method: e) Clausius-Clapeyron method. f) Virial method. g) From temperature programmed desorption (TPD). h) From differential scanning calorimetry (DSC). i) From isotherm model fit. j) Measured/calculated using an unconventional method. k) Measurement method not shown/available. m) Vant Hoff method n) Gibbs-helmholtz method S10

Physical bound explanation
This section gives some examples of attempts to correlate the empirical bound parameters and minimum heat of adsorption to physical parameters of each gas. The physical parameters used for each gas are outlined in Table S1 below.

Bound parameters
The upper and lower bounds for each gas pair are described by equation S1 (uptake vs selectivity upper bound), equation S2 (uptake vs heat of adsorption lower bound) and equation S3 (selectivity vs heat of adsorption lower bound).

( ) ( )
Where is selectivity in mol·mol -1 , is capacity in mol·kg -1 and is heat of adsorption in kJ·mol -1 . and are the fitting parameters for each bound. Figure S3, Figure S4 and Figure S5 below show the attempted correlation between these bound parameters for each gas pair and the kinetic diameter difference of the gas pair. There is no clear correlation, other physical parameters such as difference in quadrupole moment or difference in molar mass also showed no convincing physical correlation for the upper and lower bound parameters.    Figure S6, Figure S7, Figure S8, Figure S9, Figure S10 and Figure S11 below show attempts to correlate physical parameters to the estimated minimum heat of adsorption. None of the investigated parameters achieved a plausible correlation.     Figure S11: Correlation between minimum heat of adsorption and molar mass. Blue = CO 2 , orange = N 2 , green = CH 4 , red = H 2 , purple = O 2 , brown = Xe, pink = Kr, grey = Ar, olive = C 2 H 4 , cyan = C 2 H 6 , black = C 3 H 6 . S15

Other gas pairs
This section includes the bound plots of the gas pairs that did not have enough materials to perform an upper or lower bound analysis.

Choice of linear or log axis
Capacity features on a linear axis as is expected from typical isotherm models, such as the Langmuir isotherm.
In contrast, selectivity for gas A over gas B can be considered as the ratio of their equilibrium constants ( ) (also known as affinity parameters). The temperature dependence of equilibrium constants are typically expressed as an exponential function of heat of adsorption (Equation S4).

( ( ))
This can be simplified for illustrative purposes,

( )
Plotting equation S5 over a range of hypothetical values gives the curve shape in Figure S20A. Applying a log axis to Figure S20A results in Figure S20B and a linear (straight-line) plot. The upper and lower bound visualization in this work rely on linear bounds, therefore it is appropriate to use a log-axis for selectivity.

Isotherm reproducibility
This section includes the references for isotherm reproducibility sources and the isotherm reproducibility plots of HKUST-1, UiO-66 and ZIF-8.

Cost analysis
This section outlines the method used to estimate the cost of Zeolite 13X and HKUST-1. Sigma-Aldrich prices were chosen as at 5/07/2022 for the largest pack size/cheapest price per kg or L. [51] VSA adsorber vessel volume = 630 m³ Zeolite 13X density = 750 kg/m³

Zeolite 13X cost for literature example
Mass of Zeolite 13X = 472.5 tonnes Cost of Zeolite 13X quoted in paper = 5 USD/kg = 6.8USD/kg accounting for inflation.
Cost of Zeolite 13X from Alibaba = 1.5 USD/kg Total cost of Zeolite 13X = 3.2 millionUSD or 0.7 million USD.
For 1 kg of Zeolite 13X,